{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recursive least squares\n",
    "\n",
    "Recursive least squares is an expanding window version of ordinary least squares. In addition to availability of regression coefficients computed recursively, the recursively computed residuals the construction of statistics to investigate parameter instability.\n",
    "\n",
    "The `RecursiveLS` class allows computation of recursive residuals and computes CUSUM and CUSUM of squares statistics. Plotting these statistics along with reference lines denoting statistically significant deviations from the null hypothesis of stable parameters allows an easy visual indication of parameter stability.\n",
    "\n",
    "Finally, the `RecursiveLS` model allows imposing linear restrictions on the parameter vectors, and can be constructed using the formula interface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt\n",
    "from pandas_datareader.data import DataReader\n",
    "\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: Copper\n",
    "\n",
    "We first consider parameter stability in the copper dataset (description below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This data describes the world copper market from 1951 through 1975.  In an\n",
      "example, in Gill, the outcome variable (of a 2 stage estimation) is the world\n",
      "consumption of copper for the 25 years.  The explanatory variables are the\n",
      "world consumption of copper in 1000 metric tons, the constant dollar adjusted\n",
      "price of copper, the price of a substitute, aluminum, an index of real per\n",
      "capita income base 1970, an annual measure of manufacturer inventory change,\n",
      "and a time trend.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(sm.datasets.copper.DESCRLONG)\n",
    "\n",
    "dta = sm.datasets.copper.load_pandas().data\n",
    "dta.index = pd.date_range('1951-01-01', '1975-01-01', freq='AS')\n",
    "endog = dta['WORLDCONSUMPTION']\n",
    "\n",
    "# To the regressors in the dataset, we add a column of ones for an intercept\n",
    "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, construct and fit the model, and print a summary. Although the `RLS` model computes the regression parameters recursively, so there are as many estimates as there are datapoints, the summary table only presents the regression parameters estimated on the entire sample; except for small effects from initialization of the recursions, these estimates are equivalent to OLS estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:       WORLDCONSUMPTION   No. Observations:                   25\n",
      "Model:                    RecursiveLS   Log Likelihood                -154.720\n",
      "Date:                Tue, 24 Dec 2019   R-squared:                       0.965\n",
      "Time:                        15:02:05   AIC                            319.441\n",
      "Sample:                    01-01-1951   BIC                            325.535\n",
      "                         - 01-01-1975   HQIC                           321.131\n",
      "Covariance Type:            nonrobust   Scale                       117717.127\n",
      "==================================================================================\n",
      "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "const          -6562.3719   2378.939     -2.759      0.006   -1.12e+04   -1899.737\n",
      "COPPERPRICE      -13.8132     15.041     -0.918      0.358     -43.292      15.666\n",
      "INCOMEINDEX      1.21e+04    763.401     15.853      0.000    1.06e+04    1.36e+04\n",
      "ALUMPRICE         70.4146     32.678      2.155      0.031       6.367     134.462\n",
      "INVENTORYINDEX   311.7330   2130.084      0.146      0.884   -3863.155    4486.621\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                         nan   Jarque-Bera (JB):                 1.70\n",
      "Prob(Q):                               nan   Prob(JB):                         0.43\n",
      "Heteroskedasticity (H):               3.38   Skew:                            -0.67\n",
      "Prob(H) (two-sided):                  0.13   Kurtosis:                         2.53\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n"
     ]
    }
   ],
   "source": [
    "mod = sm.RecursiveLS(endog, exog)\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The recursive coefficients are available in the `recursive_coefficients` attribute. Alternatively, plots can generated using the `plot_recursive_coefficient` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[     2.88890087      4.94795049   1558.41803037   1958.43326647\n",
      " -51474.95653949  -4168.95010015  -2252.61351252   -446.55910053\n",
      "  -5288.3979429   -6942.31935003  -7846.08902378  -6643.15120355\n",
      "  -6274.11014673  -7272.01695475  -6319.02647946  -5822.239286\n",
      "  -6256.30902239  -6737.40445526  -6477.42840909  -5995.90746352\n",
      "  -6450.80677247  -6022.92165976  -5258.35152305  -5320.89135907\n",
      "  -6562.37193091]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(res.recursive_coefficients.filtered[0])\n",
    "res.plot_recursive_coefficient(range(mod.k_exog), alpha=None, figsize=(10,6));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CUSUM statistic is available in the `cusum` attribute, but usually it is more convenient to visually check for parameter stability using the `plot_cusum` method. In the plot below, the CUSUM statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.69971508  0.65841243  1.24629673  2.05476031  2.39888918  3.17861979\n",
      "  2.67244671  2.01783214  2.46131746  2.05268637  0.95054335 -1.04505547\n",
      " -2.55465287 -2.29908152 -1.45289493 -1.95353994 -1.35046621  0.15789828\n",
      "  0.63286529 -1.48184587]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(res.cusum)\n",
    "fig = res.plot_cusum();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another related statistic is the CUSUM of squares. It is available in the `cusum_squares` attribute, but it is similarly more convenient to check it visually, using the `plot_cusum_squares` method. In the plot below, the CUSUM of squares statistic does not move outside of the 5% significance bands, so we fail to reject the null hypothesis of stable parameters at the 5% level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum_squares();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 2: Quantity theory of money\n",
    "\n",
    "The quantity theory of money suggests that \"a given change in the rate of change in the quantity of money induces ... an equal change in the rate of price inflation\" (Lucas, 1980). Following Lucas, we examine the relationship between double-sided exponentially weighted moving averages of money growth and CPI inflation. Although Lucas found the relationship between these variables to be stable, more recently it appears that the relationship is unstable; see e.g. Sargent and Surico (2010)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "start = '1959-12-01'\n",
    "end = '2015-01-01'\n",
    "m2 = DataReader('M2SL', 'fred', start=start, end=end)\n",
    "cpi = DataReader('CPIAUCSL', 'fred', start=start, end=end)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ewma(series, beta, n_window):\n",
    "    nobs = len(series)\n",
    "    scalar = (1 - beta) / (1 + beta)\n",
    "    ma = []\n",
    "    k = np.arange(n_window, 0, -1)\n",
    "    weights = np.r_[beta**k, 1, beta**k[::-1]]\n",
    "    for t in range(n_window, nobs - n_window):\n",
    "        window = series.iloc[t - n_window:t + n_window+1].values\n",
    "        ma.append(scalar * np.sum(weights * window))\n",
    "    return pd.Series(ma, name=series.name, index=series.iloc[n_window:-n_window].index)\n",
    "\n",
    "m2_ewma = ewma(np.log(m2['M2SL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)\n",
    "cpi_ewma = ewma(np.log(cpi['CPIAUCSL'].resample('QS').mean()).diff().iloc[1:], 0.95, 10*4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After constructing the moving averages using the $\\beta = 0.95$ filter of Lucas (with a window of 10 years on either side), we plot each of the series below. Although they appear to move together prior for part of the sample, after 1990 they appear to diverge."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(13,3))\n",
    "\n",
    "ax.plot(m2_ewma, label='M2 Growth (EWMA)')\n",
    "ax.plot(cpi_ewma, label='CPI Inflation (EWMA)')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:               CPIAUCSL   No. Observations:                  141\n",
      "Model:                    RecursiveLS   Log Likelihood                 692.796\n",
      "Date:                Tue, 24 Dec 2019   R-squared:                       0.813\n",
      "Time:                        15:02:12   AIC                          -1381.592\n",
      "Sample:                    01-01-1970   BIC                          -1375.694\n",
      "                         - 01-01-2005   HQIC                         -1379.195\n",
      "Covariance Type:            nonrobust   Scale                            0.000\n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         -0.0033      0.001     -5.935      0.000      -0.004      -0.002\n",
      "M2             0.9098      0.037     24.584      0.000       0.837       0.982\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                     1859.31   Jarque-Bera (JB):                18.32\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               5.30   Skew:                            -0.81\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         2.29\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n"
     ]
    }
   ],
   "source": [
    "endog = cpi_ewma\n",
    "exog = sm.add_constant(m2_ewma)\n",
    "exog.columns = ['const', 'M2']\n",
    "\n",
    "mod = sm.RecursiveLS(endog, exog)\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_recursive_coefficient(1, alpha=None);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The CUSUM plot now shows substantial deviation at the 5% level, suggesting a rejection of the null hypothesis of parameter stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the CUSUM of squares shows substantial deviation at the 5% level, also suggesting a rejection of the null hypothesis of parameter stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res.plot_cusum_squares();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example 3: Linear restrictions and formulas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear restrictions\n",
    "\n",
    "It is not hard to implement linear restrictions, using the `constraints` parameter in constructing the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:       WORLDCONSUMPTION   No. Observations:                   25\n",
      "Model:                    RecursiveLS   Log Likelihood                -150.911\n",
      "Date:                Tue, 24 Dec 2019   R-squared:                       0.989\n",
      "Time:                        15:02:15   AIC                            309.822\n",
      "Sample:                    01-01-1951   BIC                            314.698\n",
      "                         - 01-01-1975   HQIC                           311.174\n",
      "Covariance Type:            nonrobust   Scale                       137155.014\n",
      "==================================================================================\n",
      "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "const          -4839.4893   2412.410     -2.006      0.045   -9567.726    -111.253\n",
      "COPPERPRICE        5.9797     12.704      0.471      0.638     -18.921      30.880\n",
      "INCOMEINDEX     1.115e+04    666.308     16.738      0.000    9847.002    1.25e+04\n",
      "ALUMPRICE          5.9797     12.704      0.471      0.638     -18.921      30.880\n",
      "INVENTORYINDEX   241.3447   2298.951      0.105      0.916   -4264.516    4747.205\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                         nan   Jarque-Bera (JB):                 1.78\n",
      "Prob(Q):                               nan   Prob(JB):                         0.41\n",
      "Heteroskedasticity (H):               1.75   Skew:                            -0.63\n",
      "Prob(H) (two-sided):                  0.48   Kurtosis:                         2.32\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 2.75e+17. Standard errors may be unstable.\n"
     ]
    }
   ],
   "source": [
    "endog = dta['WORLDCONSUMPTION']\n",
    "exog = sm.add_constant(dta[['COPPERPRICE', 'INCOMEINDEX', 'ALUMPRICE', 'INVENTORYINDEX']])\n",
    "\n",
    "mod = sm.RecursiveLS(endog, exog, constraints='COPPERPRICE = ALUMPRICE')\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formula\n",
    "\n",
    "One could fit the same model using the class method `from_formula`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                           Statespace Model Results                           \n",
      "==============================================================================\n",
      "Dep. Variable:       WORLDCONSUMPTION   No. Observations:                   25\n",
      "Model:                    RecursiveLS   Log Likelihood                -150.911\n",
      "Date:                Tue, 24 Dec 2019   R-squared:                       0.989\n",
      "Time:                        15:02:15   AIC                            309.822\n",
      "Sample:                    01-01-1951   BIC                            314.698\n",
      "                         - 01-01-1975   HQIC                           311.174\n",
      "Covariance Type:            nonrobust   Scale                       137155.014\n",
      "==================================================================================\n",
      "                     coef    std err          z      P>|z|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept      -4839.4893   2412.410     -2.006      0.045   -9567.726    -111.253\n",
      "COPPERPRICE        5.9797     12.704      0.471      0.638     -18.921      30.880\n",
      "INCOMEINDEX     1.115e+04    666.308     16.738      0.000    9847.002    1.25e+04\n",
      "ALUMPRICE          5.9797     12.704      0.471      0.638     -18.921      30.880\n",
      "INVENTORYINDEX   241.3447   2298.951      0.105      0.916   -4264.516    4747.205\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                         nan   Jarque-Bera (JB):                 1.78\n",
      "Prob(Q):                               nan   Prob(JB):                         0.41\n",
      "Heteroskedasticity (H):               1.75   Skew:                            -0.63\n",
      "Prob(H) (two-sided):                  0.48   Kurtosis:                         2.32\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Parameters and covariance matrix estimates are RLS estimates conditional on the entire sample.\n",
      "[2] Covariance matrix is singular or near-singular, with condition number 2.75e+17. Standard errors may be unstable.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\statsmodels\\tsa\\base\\tsa_model.py:165: ValueWarning: No frequency information was provided, so inferred frequency AS-JAN will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "mod = sm.RecursiveLS.from_formula(\n",
    "    'WORLDCONSUMPTION ~ COPPERPRICE + INCOMEINDEX + ALUMPRICE + INVENTORYINDEX', dta,\n",
    "    constraints='COPPERPRICE = ALUMPRICE')\n",
    "res = mod.fit()\n",
    "print(res.summary())"
   ]
  }
 ],
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